Properties

Label 2.1.2.2a1.2-1.8.38g
Base 2.1.2.2a1.2
Degree \(8\)
e \(8\)
f \(1\)
c \(38\)

Related objects

Downloads

Learn more

Defining polynomial

$x^{8} + \left(b_{39} \pi^{5} + a_{31} \pi^{4}\right) x^{7} + \left(b_{30} \pi^{4} + a_{22} \pi^{3}\right) x^{6} + b_{37} \pi^{5} x^{5} + \left(b_{20} \pi^{3} + a_{12} \pi^{2}\right) x^{4} + b_{35} \pi^{5} x^{3} + b_{26} \pi^{4} x^{2} + b_{33} \pi^{5} x + c_{40} \pi^{6} + c_{32} \pi^{5} + c_{24} \pi^{4} + \pi$

Invariants

Residue field characteristic: $2$
Degree: $8$
Base field: $\Q_{2}(\sqrt{-5})$
Ramification index $e$: $8$
Residue field degree $f$: $1$
Discriminant exponent $c$: $38$
Absolute Artin slopes: $[2,3,\frac{7}{2},4]$
Swan slopes: $[3,4,5]$
Means: $\langle\frac{3}{2},\frac{11}{4},\frac{31}{8}\rangle$
Rams: $(3,5,9)$
Field count: $216$ (complete)
Ambiguity: $8$
Mass: $128$
Absolute Mass: $64$

Diagrams

Varying

These invariants are all associated to absolute extensions of $\Q_{ 2 }$ within this relative family, not the relative extension.

Galois group: $C_4:C_4$ (show 8), $C_4 \times D_4$ (show 8), $C_2 \times (C_2^2:C_4)$ (show 4), $C_4^2:C_2$ (show 2), $C_4^2:C_2$ (show 2), $C_2^2:Q_8$ (show 12), $C_4:D_4$ (show 6), $C_2^2\wr C_2$ (show 4), $C_4:D_4$ (show 4), $C_2^2\wr C_2$ (show 2), $C_2^2.D_4$ (show 4), $C_2\wr C_2^2$ (show 4), $C_2^3.D_4$ (show 2), $C_2\wr C_2^2$ (show 2), $C_2^3.D_4$ (show 2), $C_2\wr C_2^2$ (show 4), $C_2^2:\SD_{16}$ (show 8), $C_2^2.Q_{16}$ (show 8), $C_2^3.D_4$ (show 4), $C_2\wr C_4$ (show 2), $C_2^3.D_4$ (show 4), $C_4^2:D_4$ (show 16), $C_2^4.D_4$ (show 4), $C_2^4.D_4$ (show 8), $C_2^4.D_4$ (show 4), $C_2^4.D_4$ (show 4), $C_2^4.D_4$ (show 4), $C_4^2:D_4$ (show 4), $C_4^2.D_4$ (show 8), $C_4^2:D_4$ (show 4), $C_4^2:D_4$ (show 4), $C_4^2.D_4$ (show 8), $C_4^2:D_4$ (show 8), $C_4^2:D_4$ (show 4), $C_4^2:D_4$ (show 8), $C_2^4.(C_4\times D_4)$ (show 8), $C_2^4.(C_4\times D_4)$ (show 8), $C_2^4.(C_4\times D_4)$ (show 8), $C_2^4.(C_4\times D_4)$ (show 8)
Hidden Artin slopes: $[\ ]$ (show 8), $[\ ]^{2}$ (show 48), $[2]^{2}$ (show 40), $[2,\frac{7}{2}]^{2}$ (show 48), $[2,2,\frac{7}{2}]^{4}$ (show 32), $[2]^{4}$ (show 40)
Indices of inseparability: $[39,30,20,8,0]$
Associated inertia: $[1,1,1,1]$
Jump Set: $[1,2,4,8,32]$

Fields

Galois group Galois Artin Indices
Assoc. Inertia Jump Set
Sort order Select

Showing 1-50 of 216

Next   displayed columns for results
Label Polynomial $/ \Q_p$ Galois group $/ \Q_p$ Galois degree $/ \Q_p$ $\#\Aut(K/\Q_p)$ Artin slope content $/ \Q_p$ Swan slope content $/ \Q_p$ Hidden Artin slopes $/ \Q_p$ Hidden Swan slopes $/ \Q_p$ Ind. of Insep. $/ \Q_p$ Assoc. Inertia $/ \Q_p$ Resid. Poly Jump Set
2.1.16.54o1.217 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{11} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 6$ $C_4^2.D_4$ (as 16T344) $128$ $4$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.218 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{11} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 22$ $C_4^2.D_4$ (as 16T344) $128$ $4$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.219 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{11} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 22$ $C_4^2:D_4$ (as 16T340) $128$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.220 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 22$ $C_4^2:D_4$ (as 16T340) $128$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.221 $x^{16} + 8 x^{15} + 4 x^{14} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 6$ $C_4^2.D_4$ (as 16T344) $128$ $4$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.222 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 22$ $C_2^4.D_4$ (as 16T326) $128$ $2$ $[2, 2, 3, \frac{7}{2}, 4]^{4}$ $[1,1,2,\frac{5}{2},3]^{4}$ $[2]^{4}$ $[1]^{4}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.223 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 22$ $C_2^4.D_4$ (as 16T326) $128$ $2$ $[2, 2, 3, \frac{7}{2}, 4]^{4}$ $[1,1,2,\frac{5}{2},3]^{4}$ $[2]^{4}$ $[1]^{4}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.224 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{11} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 22$ $C_2^2\wr C_2$ (as 16T46) $32$ $4$ $[2, 3, \frac{7}{2}, 4]^{2}$ $[1,2,\frac{5}{2},3]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.225 $x^{16} + 4 x^{14} + 8 x^{11} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 22$ $C_4:D_4$ (as 16T34) $32$ $4$ $[2, 3, \frac{7}{2}, 4]^{2}$ $[1,2,\frac{5}{2},3]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.226 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{11} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 6$ $C_4 \times D_4$ (as 16T19) $32$ $8$ $[2, 3, \frac{7}{2}, 4]^{2}$ $[1,2,\frac{5}{2},3]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.227 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{11} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 22$ $C_4 \times D_4$ (as 16T19) $32$ $8$ $[2, 3, \frac{7}{2}, 4]^{2}$ $[1,2,\frac{5}{2},3]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.228 $x^{16} + 4 x^{14} + 8 x^{13} + 8 x^{11} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 22$ $C_2^2:Q_8$ (as 16T31) $32$ $8$ $[2, 3, \frac{7}{2}, 4]^{2}$ $[1,2,\frac{5}{2},3]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.229 $x^{16} + 8 x^{15} + 4 x^{14} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 22$ $C_4^2.D_4$ (as 16T344) $128$ $4$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.230 $x^{16} + 4 x^{14} + 8 x^{13} + 8 x^{11} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 6$ $C_2^2:Q_8$ (as 16T31) $32$ $8$ $[2, 3, \frac{7}{2}, 4]^{2}$ $[1,2,\frac{5}{2},3]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.231 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 22$ $C_4^2:D_4$ (as 16T400) $128$ $4$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.232 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{11} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 22$ $C_4^2:D_4$ (as 16T402) $128$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.233 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{11} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 6$ $C_4^2:D_4$ (as 16T400) $128$ $4$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.234 $x^{16} + 4 x^{14} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 22$ $C_2^2\wr C_2$ (as 16T39) $32$ $8$ $[2, 3, \frac{7}{2}, 4]^{2}$ $[1,2,\frac{5}{2},3]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.235 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 22$ $C_4:D_4$ (as 16T43) $32$ $8$ $[2, 3, \frac{7}{2}, 4]^{2}$ $[1,2,\frac{5}{2},3]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.236 $x^{16} + 4 x^{14} + 8 x^{13} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 6$ $C_4:C_4$ (as 16T8) $16$ $16$ $[2, 3, \frac{7}{2}, 4]$ $[1,2,\frac{5}{2},3]$ $[\ ]$ $[\ ]$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.237 $x^{16} + 4 x^{14} + 8 x^{13} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 22$ $C_4:C_4$ (as 16T8) $16$ $16$ $[2, 3, \frac{7}{2}, 4]$ $[1,2,\frac{5}{2},3]$ $[\ ]$ $[\ ]$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.238 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 22$ $C_2^2.D_4$ (as 16T54) $32$ $8$ $[2, 3, \frac{7}{2}, 4]^{2}$ $[1,2,\frac{5}{2},3]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.239 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 22$ $C_2^3.D_4$ (as 16T177) $64$ $4$ $[2, 2, 3, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},3]^{2}$ $[2]^{2}$ $[1]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.240 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 22$ $C_2\wr C_2^2$ (as 16T150) $64$ $4$ $[2, 2, 3, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},3]^{2}$ $[2]^{2}$ $[1]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.241 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{11} + 10 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 6$ $C_4^2:D_4$ (as 16T400) $128$ $4$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.242 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{11} + 10 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 22$ $C_4^2:D_4$ (as 16T402) $128$ $2$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.243 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{11} + 10 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 22$ $C_4^2:D_4$ (as 16T400) $128$ $4$ $[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ $[2,\frac{7}{2}]^{2}$ $[1,\frac{5}{2}]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.244 $x^{16} + 4 x^{14} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 22$ $C_4:D_4$ (as 16T43) $32$ $8$ $[2, 3, \frac{7}{2}, 4]^{2}$ $[1,2,\frac{5}{2},3]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.245 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 22$ $C_2^2\wr C_2$ (as 16T39) $32$ $8$ $[2, 3, \frac{7}{2}, 4]^{2}$ $[1,2,\frac{5}{2},3]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.246 $x^{16} + 4 x^{14} + 8 x^{13} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 22$ $C_2^2.D_4$ (as 16T54) $32$ $8$ $[2, 3, \frac{7}{2}, 4]^{2}$ $[1,2,\frac{5}{2},3]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.247 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 6$ $C_4:C_4$ (as 16T8) $16$ $16$ $[2, 3, \frac{7}{2}, 4]$ $[1,2,\frac{5}{2},3]$ $[\ ]$ $[\ ]$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.248 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 22$ $C_4:C_4$ (as 16T8) $16$ $16$ $[2, 3, \frac{7}{2}, 4]$ $[1,2,\frac{5}{2},3]$ $[\ ]$ $[\ ]$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.249 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{11} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 22$ $C_2^3.D_4$ (as 16T177) $64$ $4$ $[2, 2, 3, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},3]^{2}$ $[2]^{2}$ $[1]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.250 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{11} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 22$ $C_2\wr C_2^2$ (as 16T150) $64$ $4$ $[2, 2, 3, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},3]^{2}$ $[2]^{2}$ $[1]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.251 $x^{16} + 4 x^{14} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 22$ $C_2^3.D_4$ (as 16T165) $64$ $4$ $[2, 2, 3, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},3]^{2}$ $[2]^{2}$ $[1]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.252 $x^{16} + 8 x^{15} + 4 x^{14} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 22$ $C_2^3.D_4$ (as 16T165) $64$ $4$ $[2, 2, 3, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},3]^{2}$ $[2]^{2}$ $[1]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.253 $x^{16} + 4 x^{14} + 8 x^{13} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 22$ $C_2\wr C_2^2$ (as 16T129) $64$ $4$ $[2, 2, 3, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},3]^{2}$ $[2]^{2}$ $[1]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.254 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 22$ $C_2\wr C_2^2$ (as 16T129) $64$ $4$ $[2, 2, 3, \frac{7}{2}, 4]^{2}$ $[1,1,2,\frac{5}{2},3]^{2}$ $[2]^{2}$ $[1]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.255 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{11} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 22$ $C_4:D_4$ (as 16T34) $32$ $4$ $[2, 3, \frac{7}{2}, 4]^{2}$ $[1,2,\frac{5}{2},3]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.256 $x^{16} + 4 x^{14} + 8 x^{11} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 22$ $C_2^2:Q_8$ (as 16T31) $32$ $8$ $[2, 3, \frac{7}{2}, 4]^{2}$ $[1,2,\frac{5}{2},3]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.257 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{11} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 6$ $C_2 \times (C_2^2:C_4)$ (as 16T21) $32$ $8$ $[2, 3, \frac{7}{2}, 4]^{2}$ $[1,2,\frac{5}{2},3]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.258 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{11} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 22$ $C_2 \times (C_2^2:C_4)$ (as 16T21) $32$ $8$ $[2, 3, \frac{7}{2}, 4]^{2}$ $[1,2,\frac{5}{2},3]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.259 $x^{16} + 4 x^{14} + 8 x^{13} + 8 x^{11} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 22$ $C_4:D_4$ (as 16T34) $32$ $4$ $[2, 3, \frac{7}{2}, 4]^{2}$ $[1,2,\frac{5}{2},3]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.260 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{11} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 6$ $C_2^4.(C_4\times D_4)$ (as 16T926) $512$ $2$ $[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ $[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ $[2,2,\frac{7}{2}]^{4}$ $[1,1,\frac{5}{2}]^{4}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.261 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{11} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 6$ $C_2^4.(C_4\times D_4)$ (as 16T926) $512$ $2$ $[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ $[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ $[2,2,\frac{7}{2}]^{4}$ $[1,1,\frac{5}{2}]^{4}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.262 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{11} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 22$ $C_2^4.(C_4\times D_4)$ (as 16T926) $512$ $2$ $[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ $[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ $[2,2,\frac{7}{2}]^{4}$ $[1,1,\frac{5}{2}]^{4}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.263 $x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 8 x^{11} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 22$ $C_2^4.(C_4\times D_4)$ (as 16T926) $512$ $2$ $[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ $[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ $[2,2,\frac{7}{2}]^{4}$ $[1,1,\frac{5}{2}]^{4}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.264 $x^{16} + 4 x^{14} + 8 x^{11} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 6$ $C_2^2:Q_8$ (as 16T31) $32$ $8$ $[2, 3, \frac{7}{2}, 4]^{2}$ $[1,2,\frac{5}{2},3]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.265 $x^{16} + 8 x^{15} + 4 x^{14} + 10 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 8 x^{2} + 22$ $C_2^2:Q_8$ (as 16T31) $32$ $8$ $[2, 3, \frac{7}{2}, 4]^{2}$ $[1,2,\frac{5}{2},3]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
2.1.16.54o1.266 $x^{16} + 4 x^{14} + 10 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 8 x^{2} + 22$ $C_4^2:C_2$ (as 16T27) $32$ $4$ $[2, 3, \frac{7}{2}, 4]^{2}$ $[1,2,\frac{5}{2},3]^{2}$ $[\ ]^{2}$ $[\ ]^{2}$ $[39, 30, 20, 8, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 2, 4, 8, 32]$
Next   displayed columns for results